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The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

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179<br />

(C.16)<br />

l�r-2. (C.17)<br />

h + l2 = r - /'i, - 2q - j � r - 2 . (C.18)<br />

In the last <strong>in</strong>equality we have used the same arguments as for the case ,\0 HK,,\4 q +j Al'r), from<br />

w hich follows that 2q + j + /'i, 2': 2 for all q, j.<br />

We also exam<strong>in</strong>e the cases with ,\ o -<strong>in</strong>termediate cases:<br />

1. k = 0, i # 0<br />

<strong>The</strong> <strong>in</strong>equality (A.4) leads to<br />

2. k> 1<br />

From eq. (A.6) we obta<strong>in</strong><br />

l = r + 2k + i - /'i, • (C.19)<br />

l � r . (C.20)<br />

l � r. (C.21)<br />

h + l2 = r - /'i, � r - 2 .<br />

(C.22)

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